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Laplace Transform is widely used by electronic engineers to solve quickly differential equations occurring in the analysis of electronic circuits 2 System modeling:

Laplace transform is an integral transform method which is particularly useful in solving linear ordinary dif- ferential equations It finds very wide applications in var-

[PDF] APPLICATIONS OF LAPLACE TRANSFORM IN - IRJET

Laplace Transform is widely used by electronic engineers to solve quickly differential equations occurring in the analysis of electronic circuits 2 System modeling:

[PDF] Review of Laplace Transform and Its Applications in Mechanical

To learn the application of Laplace transform in engineering analysis ○ To learn the required conditions to transform variable or variables in functions by

[PDF] LAPLACE TRANSFORMS AND THEIR APPLICATIONS

Another important application of Laplace Transform is in finding the solution of Mathematical Model of physical problem where in the right hand of the differential

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Laplace Transform and its application for solving differential equations Fourier and Z Transforms Motivation Transform methods are widely used in many areas

APPLICATION OF LAPLACE TRANSFORM - ScienceDirectcom

Pipes [I], for example, has applied an operational method based on the Laplace transform for solving non-linear equations Ames [2] describes an iterative

[PDF] LAPLACE TRANSFORM AND ITS APPLICATIONS

function like the Heaviside's Unit Step Function and the Dirac Delta Function A few practical life applications of Laplace Transform have also been stated

[PDF] The Laplace Transform: Theory and Applications - ResearchGate

The Laplace transform is a wonderful tool for solving ordinary and partial differential equations and has enjoyed much success in this realm With its success,

[PDF] Applications of Laplace Transformation in Engineering Field

Like the Fourier transform, the Laplace transform is used for solving differential and integral equations In physics and engineering, it is used for analysis of linear

[PDF] APPLICATIONS OF LAPLACE TRANSFORM IN - IRJET

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056

Volume: 05 Issue: 05 | May-2018 www.irjet.net p-ISSN: 2395-0072

APPLICATIONS OF LAPLACE TRANSFORM IN ENGINEERING FIELDS

Prof. L.S. Sawant

Asst. Professor, Department of Mathematics, DKTE 3...-ǯ Textile & Eng. Institute, Ichalkaranji,

Maharashtra, India,

Abstract: In this paper, we will discuss about applications of Laplace Transform in different engineering fields. Also we discuss about how to solve differential equations by using Laplace Transform. How to find transfer function of mechanical system, How to use Laplace Transform in nuclear physics as well as Automation engineering, Control engineering and Signal processing.

Key Words:

Laplace Transform, Differential Equation, Inverse

Laplace Transform, Linearity, Convolution Theorem.

1. INTRODUCTION

The Laplace Transform is a widely used integral transform in mathematics with many applications in science and engineering. The Laplace Transform can be interpreted as a transformation from time domain where inputs and outputs are functions of time to the frequency domain where inputs and outputs are functions of complex angular frequency. Laplace Transform methods have a key role to play in the modern approach to the analysis and design of engineering system. The concepts of Laplace Transforms are applied in the area of science and technology such as Electric circuit analysis, Communication engineering, Control engineering and Nuclear physics etc.

1.1 Definition and important properties of Laplace

Transform:

The definition and some useful properties of Laplace Transform which we have to use further for solving problems related to Laplace Transform in different engineering fields are listed as follows.

Definition:

Let be a function of t , then the integral is called Laplace Transform of

We denote it as

or i.e.

1.2 Properties of Laplace Transform:

Linearity Property: If

and are any two functions of and are any two constant then,

Shifting Property:

If then

Multiplication by

Property:

then

Laplace Transform of Derivative:

If then Laplace Transform of ǯ function: , where is called ǯ function.

Inverse Laplace Transform:

then is called inverse Laplace Transform of

Inverse Laplace Transform by Convolution Theorem:

If then,

2 .Applications of Laplace Transform in Science and

Engineering fields:

This section describes the applications of Laplace Transform in the area of science and engineering. The Laplace

Transform is widely used in following science and

engineering field. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056

Volume: 05 Issue: 05 | May-2018 www.irjet.net p-ISSN: 2395-0072

1. Analysis of electronic circuits:

Laplace Transform is widely used by electronic

engineers to solve quickly differential equations occurring in the analysis of electronic circuits.

2. System modeling:

Laplace Transform is used to simplify calculations in system modeling, where large number of differential equations are used.

3. Digital signal processing:

One can not imagine solving digital signal processing problems without employing Laplace Transform.

4. Nuclear Physics:

In order to get the true form of radioactive decay a

Laplace Transform is used. It makes easy to study

analytic part of Nuclear physics possible.

5. Process Control:

Laplace Transform is used for process controls. It helps to analyze the variables which when altered, produce desired manipulations in the result. Some of the examples in science and engineering fields in which Laplace Transforms are used to solve the differential equations occurred in this fields.The following examples highlights the importance of Laplace

Transform in different engineering fields.

2.1 Laplace Transform to solve Differential Equation:

Ordinary differential equation can be easily solved by the Laplace Transform method without finding the general solution and the arbitrary constants. The method is illustrated by following example,

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